The classical coherent optical correlator is usually configured as a system with a linear dimension of 4 f, where f is the focal length of each of the two Fourier transform (FT) lenses. This configuration is shown in FIG. 1, where P.sub.1 is the input plane, L.sub.1 is the first FT lens with focal length f.sub.1, P.sub.2 is the Fourier or filter plane, L.sub.2 is the inverse FT lens with focal length f.sub.2, and P.sub.3 is the output or correlation plane. The focal length of the FT lenses must be selected according to the wavelength of light used and the size of the input object at P.sub.1 and the filter at P.sub.2. Frequently, spatial light modulators (SLMs) are used in both planes P.sub.1 and P.sub.2 for real time processing, using phase-only filter technology. See J. L. Horner and P. D. Gianino, "Phase-Only Matched Filtering," Appl. Opt. 23, 812-816 (1984) and J. L. Horner and J. R. Leger, "Pattern Recognition with Binary Phase-Only Filter," Appl. Opt. 24 609-611 (1985). See also U.S. Pat. No. 4,765,714 to Horner. It has been shown that the focal length of lens L.sub.1 must be ##EQU1## where f.sub.1 is the required focal length of the first FT lens, d.sub.1 and d.sub.2 are the pixel size of the SLM in the input and filter planes, N.sub.2 is the number of pixels in the filter SLM, and is the wavelength of light. For example, for the "Semetex" (TM) 128.times.128 Magneto-Optic SLM, N.sub.2 =128, d.sub.1 =d.sub.2 =76 m,=632.8 nm (He-Ne), and Eq. (1) gives a focal length f.sub.1 of 117 cm, or a 4 f length of over 4.5 m which is too long to be practical.
Flannery et al. proposed a system using two-element telephoto lenses for L.sub.1 and L.sub.2 that reduced the basic correlator length to 2 f. See D. L. Flannery et al., "Real-Time Coherent Correlator Using Binary Magnetooptic Spatial Light Modulators at Input and Fourier Planes," Appl. Opt. 25, 466 (1986). The system had another desirable feature in that it allowed the scale of the Fourier transform to be continuously varied, thus allowing for an exact size match between the input and filter SLM and compensating for any errors in measuring the focal length of the actual lenses used. VanderLugt also considered the information storage capacity of a 2 f holographic system. See A. VanderLugt, "Packing Density in Holographic Systems," Appl. Opt. 14, 1081-1087 (1975).